-Capacity and -Hyperbolicity of Submanifolds.
Parallel immersions into spaces of constant curvature and conformal transformations.
Parallel Kaehler Submanifolds of Hermitian Symmetric Spaces.
Paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds and semi-Riemannian submersions
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds.
Plateau-Stein manifolds
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Plongements bilipschitziens dans les espaces euclidiens, -courbure et flot quasi-conforme
Soit la métrique riemannienne standard sur et soit une déformation conforme lisse de . Nous présentons une condition suffisante en terme de -courbure pour que la variété se plonge de façon bilipschitzienne, en tant qu’espace métrique, dans . Ce théorème du à Bonk, Heinonen et Saksman découle d’un résultat lié au problème du jacobien quasiconforme.
Principal toroidal bundles over Cauchy-Riemann products.
Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform.
Projections of transnormal twisted spheres
Projective Curvature Tensorin 3-dimensional Connected Trans-Sasakian Manifolds
The object of the present paper is to study -projectively flat and -projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.
Projective subspaces in the variety of normal sections and tangent spaces to a symmetric space.
Pseudo-Bochner-flat locally conformal Kähler submanifolds
Let M̃ be an (m+r)-dimensional locally conformal Kähler (l.c.K.) manifold and let M be an m-dimensional l.c.K. submanifold of M̃ (i.e., a complex submanifold with the induced l.c.K. structure). Assume that both M̃ and M are pseudo-Bochner-flat. We prove that if r < m, then M is totally geodesic (in the Hermitian sense) in M̃. This is the l.c.K. version of Iwatani's result for Bochner-flat Kähler submanifolds.
Pseudo-parallel submanifolds of a space form.
Pseudo-umbilical spacelike submanifolds in the indefinite space form.